Using Prime Numbers to Manage Partitioning in a Cluster of Nodes of Computers

1. A method, comprising: assigning, to a first computer in a cluster of computers via a cluster management program executed by the first computer, a first unique prime number relative to unique prime numbers assigned to other computers in the cluster of computers, where the computers in the cluster of computers manage their own active partition determination in response to partitioning of the cluster using the assigned unique prime numbers; and via the cluster management program executed by the first computer: detecting a partitioning event of the cluster into a plurality of partitions, each partition comprising at least one computer of the cluster; calculating a partition value, for each partition, from a product of the unique prime numbers assigned to each computer in each partition; determining, based upon the calculated partition value for each partition, an active partition, the active partition having a greatest partition value; and enabling the first computer to provide cluster services if the first computer is within the active partition; and where the first computer makes its own determination as to whether it is part of the active partition, and calculating partition values from the product of the unique prime numbers ensures that each partition value is unique and that only one partition is enabled as the active partition.

2. The method according to claim 1 , further comprising storing, at the first computer, the unique prime numbers assigned to the other computers in the cluster.

3. The method according to claim 1 , further comprising receiving, at the first computer, a second unique prime number for a new computer to the cluster, the second unique prime number being a lowest prime number not assigned to any other computer in the cluster.

4. The method according to claim 1 , further comprising storing, at the first computer, a table of unique identifiers and the unique prime numbers associated with the other computers in the cluster.

5. The method according to claim 1 , further comprising: disabling the first computer from providing the cluster services if the first computer is not within the active partition; and designating other computers not in the active partition as inactive computers.

6. The method according to claim 1 , further comprising: calculating a number of computers in each partition, the active partition comprising a partition having a largest number of computers; and if more than one partition has the largest number of computers, then the active partition comprises a partition having the largest number of computers and having the greatest partition value.

7. The method according to claim 1 , where assigning, to the first computer in the cluster of computers via the cluster management program executed by the first computer, the first unique prime number relative to the unique prime numbers assigned to the other computers in the cluster of computers comprises: providing a first and a second range of unique prime numbers, the second range being greater than the first range, the first unique prime number being assigned in the second range to increase a probability of the first computer being in the active partition.

8. The method according to claim 1 , in which a number of bits used to represent the first unique prime number is moderated within a predetermined limit.

9. An apparatus, comprising: an interface to a cluster interconnect for interconnecting a first computer to a cluster of computers; and a processor of the first computer coupled to the interface to the cluster interconnect and programmed to execute a cluster management program, where the processor is programmed to: assign to the first computer in the cluster of computers a first unique prime number relative to unique prime numbers assigned to other computers in the cluster of computers, where the computers in the cluster of computers manage their own active partition determination in response to partitioning of the cluster using the assigned unique prime numbers; detect a partitioning event of the cluster into a plurality of partitions, each partition comprising at least one computer of the cluster; calculate a partition value, for each partition, from a product of the unique prime numbers assigned to each computer in each partition; determine, based upon the calculated partition value for each partition, an active partition, the active partition having a greatest partition value; and enable the first computer to provide cluster services if the first computer is within the active partition; and where the first computer makes its own determination as to whether it is part of the active partition, and calculating partition values from the product of the unique prime numbers ensures that each partition value is unique and that only one partition is enabled as the active partition.

10. The apparatus according to claim 9 , where the processor is further programmed to store the unique prime numbers assigned to the other computers in the cluster.

11. The apparatus according to claim 9 , where the processor is further programmed to receive a second unique prime number for a new computer to the cluster, the second unique prime number being a lowest prime number not assigned to any other computer in the cluster.

12. The apparatus according to claim 9 , where the processor is further programmed to store a table of unique identifiers and the unique prime numbers associated with the other computers in the cluster.

13. The apparatus according to claim 9 , where the processor is further programmed to: disable the first computer from providing the cluster services if the first computer is not within the active partition; and designate other computers not in the active partition as inactive computers.

14. The apparatus according to claim 9 , where the processor is further programmed to: calculate a number of computers in each partition, the active partition comprising a partition having a largest number of computers; and if more than one partition has the largest number of computers, then the active partition comprises a partition having the largest number of computers and having the greatest partition value.

15. The apparatus according to claim 9 , where the processor, in being programmed to assign to the first computer in the cluster of computers the first unique prime number relative to the unique prime numbers assigned to the other computers in the cluster of computers, is programmed to provide a first and a second range of unique prime numbers, the second range being greater than the first range, the first unique prime number being assigned in the second range to increase a probability of the first computer being in the active partition.

16. A computer program product comprising a computer readable storage device having computer readable program code tangibly embodied therewith, where the computer readable program code when executed on a computer causes the computer to: assign, to the computer in a cluster of computers, a first unique prime number relative to unique prime numbers assigned to other computers in the cluster of computers, where the computers in the cluster of computers manage their own active partition determination in response to partitioning of the cluster using the assigned unique prime numbers; detect a partitioning event of the cluster into a plurality of partitions, each partition comprising at least one computer of the cluster; calculate a partition value, for each partition, from a product of the unique prime numbers assigned to each computer in each partition; determine based upon the calculated partition value for each partition, an active partition, the active partition having a greatest partition value; and enable the computer to provide cluster services if the computer is within the active partition; and where the computer makes its own determination as to whether it is part of the active partition, and calculating partition values from the product of the unique prime numbers ensures that each partition value is unique and that only one partition is enabled as the active partition.

17. The computer program product of claim 16 , further comprising computer readable program code configured to store, at the computer, a table of unique identifiers and the unique prime numbers associated with the other computers in the cluster.

18. The computer program product of claim 16 , where the computer readable program code configured to assign, to the computer in the cluster of computers, the first unique prime number relative to the unique prime numbers assigned to the other computers in the cluster of computers comprises computer readable program code configured to provide a first and a second range of unique prime numbers, the second range being greater than the first range, the first unique prime number being assigned in the second range to increase a probability of the computer being in the active partition.